Thermo-mechanical stability of FRP and FGM plates with geometrical imperfections using layer wise finite element

Abstract

One of the ultimate limit state important for the safe design of structures is failure due to buckling. The origin of buckling, as the sudden change in shape of structural component, may arise from mechanical as well from thermal loading conditions. Apart from the loading conditions, the geometrical imperfections are another parameter important for the overall structural stability. In wish to fulfil the lack of thermo-mechanical stability solutions based on Layer Wise (LW) plate theories, which will be able to include general form of geometrical imperfection, this study presents the LW finite element for thermo-mechanical stability of geometrically imperfect FRP (Fibre reinforced polymer) and FGM (Functionally Graded Material) plates. The mathematical model, based on Layer wise theory of Reddy, assumes layer wise variation of in plane displacements and constant transverse displacement through the thickness, non-linear strain displacement relations and isotropic/orthotropic material properties. The material properties of FGM plates are assumed to be constant in xy-plane and vary through the thickness by a power law function in terms of the volume fraction of the constituents. The Koiter’s model for initial geometric imperfection is adopted. The principle of virtual displacement (PVD) is utilized to derive Euler-Lagrange differential equation of linearized buckling problem. The weak form is discretized using nine node Lagrangian isoparametric finite element. The original MATLAB computer program is coded for the finite element solution and used to study influence of plate thickness a/h, aspect ratio a/b, power low index, imperfection form and material properties on thermo-mechanical stability of FRP and FGM plates. The results are compared with the one from the literature.